You asked about Alexander in the 1800s.I can't give you that but here is a disccusion of the Jewish name Alexander for the 1500s.
SCOTTISH ALEXANDERS "The Alexanders arrived in Scotland in the late 1400s or early 1500s, concurrent with the Spanish and Portuguese inquisitions (Roth 1937).Further, both as a given name and surname, Alexander is not indigenous to the British Isles.Rather it is Greek in origin and was one of the most widely used names among Mediterranean Jews in the Middle Ages (Roth 1937).The Alexander family settled in the southwestern portion of Scotland, near Stirling on the English border--a locale with easy access to France and the ports of the Mediterranean.The lineage of the Alexander Earls of Stirling is instructive in showing a pattern of intermarriage with other DNA-confirmed Sephardic-Scottish families (e.g., Forbes, Douglas)."(Hirschman & Yates, 74-75.)
"According to the U.S. Census for 1990, Alexander iss the 96th most common surname in America.If you add the variants Sanders (75th) and Saunders (421st), the frequency climbs to .2 percent, rather high in the scheme of things.However, Alexander is even more common as a specifically Jewish surname.It is among the top ten researched surnames at the Jewish Genealogial Society of Great Britain, and it figures prominently in Rabbi Malcolm Stern's Americans of Jewish Descent (1991), as well as in studies of Jewish tombstones in Barbados and Jamaica by Barnett (1959) and Wright (1976).The Alexander genealogical manuscripts of the American Jewish Historical Society are voluminous."(75.)
SOURCES 1.Elizabeth Caldwell Hirschman and Donald N. Yates.When Scotland Was Jewish.Jefferson, North, Carolina: McFarland Publishers, 2007.This book would be available forsale and also through interlibrary loan.My copy came from the University of Chicago, one of its libraries.